An object is held in the air 30m above ground and released. Assume the drag forc

Question

An object is held in the air 30m above ground and released. Assume the drag force due to air resistance is given by Fd = 1.0Vy. What is the mass of the object necessary so that it reaches ground in 3s ? What is its velocity when it hits ground?

This is what I have so far...

Summation Fy = mAy

m dVy/dt = Summation Fy   (1) 1 eq. 3 unknown [m,Vy,Summation Fy]

Summation Fy =Fg + Fd => -mg - 1.0Vy (2) 2 eq. 3 unknown

m dVy/dt = -mg - Vy   (3) 1 eq. 2 unknown [m,Vy]

dy/dt = Vy      (4) 2 eq. 3 unknown [y]

y(3) = 0    (5) 3 eq. 3 unknown

From (equation 3):

m dVy/dt = -(1)(mg + Vy)

m*integral of (dVy/(mg+Vy) = - integral of (dt) From 0 to Vy and 0 to t

Explanation / Answer

m dv/dt = F = mg - v

m dv/(mg - v) = dt

integrate,

m ln|mg - v| = -t + C

use t = 0, v = 0, so C = m ln|mg|

m ln|(mg - v)/(mg)| = -t

v = mg(1 - e-t/m) (1)

dy/dt = mg(1 - e-t/m)

y = mg(t + me-t/m)]

plug y = 30 m, t = 3 s,

solve 30 = 9.81m(3 + me-3/m) and get m = 1.00 kg

plug it and t = 3 s into (1) and get v = 1*9.81*(1 - e-3/1) = 9.32 m/s

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.